SyzygyData

Current Betti Table Entry:

\(n=2\)

\(d=2\)

\(b=1\)

\(p=1\)

\(q=0\)

0 1 2 3
0 3 8 6 ·
1 · · · 1
2 · · · ·
0 1 2 3
0 (1,0,0) (2,1,0) (3,1,1) ·
1 · · · (3,3,3)
2 · · · ·
0 1 2 3
0 1 1 1 ·
1 · · · 1
2 · · · ·
0 1 2 3
0 1 1 1 ·
1 · · · 1
2 · · · ·

Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{1,\lambda}(2,1;2)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{1,0}(2,1;2)\). Here \(\lambda\) is the weight \((\lambda_0,\lambda_1,\lambda_2)\) where \(\lambda_2\) is determined by the fact that \(|\lambda|\) equals \(d(p+q)+b\). The dominant weights are displayed in green. Click on an entry for more info!

1 2 3
0 · · ·
1 · 1 ·
2 · · ·

Below is a plot displaying the multigraded Betti numbers. In the \((a_0,a_1)\) spot we place \(\beta_{1,\textbf{a}}(2,1;2)\). Here \(\textbf{a}\) is the weight \((a_0,a_1,a_2)\) where \(a_2\) is determined by the fact that \(|\textbf{a}|\) equals \(d(p+q)+b\). Entries with error corrected via our Schur decomposition algorithm are in orange. Click on an entry for more info!

0 1 2 3
0 · 1 1 ·
1 1 2 1 ·
2 1 1 · ·
3 · · · ·